Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+y &= 7 \\ -x-y &= 1\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = y+1$ Divide both sides by $-1$ to isolate $x$ $x = {-y - 1}$ Substitute this expression for $x$ in the first equation. $-6({-y - 1}) + y = 7$ $6y + 6 + y = 7$ Simplify by combining terms, then solve for $y$ $7y + 6 = 7$ $7y = 1$ $y = \dfrac{1}{7}$ Substitute $\dfrac{1}{7}$ for $y$ in the top equation. $-6x+ \dfrac{1}{7} = 7$ $-6x+\dfrac{1}{7} = 7$ $-6x = \dfrac{48}{7}$ $x = -\dfrac{8}{7}$ The solution is $\enspace x = -\dfrac{8}{7}, \enspace y = \dfrac{1}{7}$.